Invariants
Base field: | $\F_{2^{4}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 5 x + 16 x^{2} )( 1 - 4 x + 16 x^{2} )$ |
$1 - 9 x + 52 x^{2} - 144 x^{3} + 256 x^{4}$ | |
Frobenius angles: | $\pm0.285098958592$, $\pm0.333333333333$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $0$ |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
$p$-rank: | $1$ |
Slopes: | $[0, 1/2, 1/2, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $156$ | $72072$ | $17795700$ | $4342338000$ | $1098937569756$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $8$ | $280$ | $4340$ | $66256$ | $1048028$ | $16763992$ | $268386308$ | $4294949536$ | $68720108780$ | $1099514547880$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{12}}$.
Endomorphism algebra over $\F_{2^{4}}$The isogeny class factors as 1.16.af $\times$ 1.16.ae and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
The base change of $A$ to $\F_{2^{12}}$ is 1.4096.el $\times$ 1.4096.ey. The endomorphism algebra for each factor is:
|
Base change
This is a primitive isogeny class.